The most efficient output of a firm is located (LO1, 7) a) at the shut-down point b) at the break-even point c) where \(\mathrm{MC}=\mathrm{MR}\) d) when the vertical distance between AVC and ATC is at a maximum

: 1. Shut-down point: This is the point at which the price of a good falls below the minimum value of the average variable cost. When this occurs, a firm will choose to temporarily shut down, as it would be incurring a loss if it continued production. 2. Break-even point: This is the production level at which total costs equal total revenues. At this point, the firm is not making any profit, but it is also not incurring any losses. 3. Marginal cost (MC): The additional cost incurred while producing one more unit of a good. 4. Marginal revenue (MR): The additional revenue a firm gets from selling one more unit of a good. 5. Average variable cost (AVC): The total variable cost per unit of output. 6. Average total cost (ATC): The total cost per unit of output, which includes both variable and fixed costs.

: Now we'll compare the given options to determine the most efficient output for a firm: a) Shut-down point: At this point, a firm decides to temporarily shut down, so this can't be the most efficient output. b) Break-even point: At this point, the firm is not making any profit, but it is also not incurring any losses. While it's better than the shut-down point, it doesn't guarantee efficiency. c) Where MC = MR: This is the condition to maximize a firm's profit. When MC equals MR, a firm is producing at the most efficient output level. Any additional unit of production would increase cost more than revenue, leading to a decrease in profit. d) The vertical distance between AVC and ATC at a maximum: While there is a connection between costs and efficiency, the vertical distance between AVC and ATC doesn't provide any information about a firm's efficiency regarding profits or output levels.

: From the analysis of the given options, we can conclude that the most efficient output of a firm is located where \(MC=MR\). Therefore, the correct answer is option (c).